Look at the drawing below, where AB = BC = CD = DT = h, and TD perpendicular to AD:
o T

 (h)


+++o
A (h) B (h) C (h) D
The line AT makes an angle x with AD; the line BT makes an angle y with BD; the line CT makes an angle z with CD.
Using
only geometry, prove that (angle x) + (angle y) = (angle z).
1 1
 + 
tan(x) + tan(y) 3 2
tan(x+y) =  =  = 1 = tan(z)
1  tan(x)*tan(y) 1 1
1  x
3 2
Therefore, z = x+y

Posted by Bractals
on 20051224 03:41:34 